I think the best response you could have given your daughter on what to tell people is that it is a private family matter and she prefer not to discuss it.
I am not suggesting you lie to your kids but once again your daughter is put in the middle of an adult issue between you and your W. There really is no reason to cover up anything your W is doing because you should not be talking about your W with your kids at all.
You cant control what your W tells people. And it is good you dont care what W thinks anymore but for you its "tit for tat"... she doesnt care about you so you wont care about her and you "not caring" seems to always involve your kids and putting them in the middle. You *will* have to co-parent with this woman for many yrs to come so I think you need to change yoru outlook.
If you really dont care what your W thinks anymore then why do you care if she says she is divorced?
And where exactly has this "tit for tat" approach gotten you thus far? Not that far that I can see.